1) Given that sinA=-8/17 and CosB=4/5 with A in quadrant 3 a

[WolfSpice]

1) Given that sinA=-8/17 and CosB=4/5 with A in quadrant 3 and B in quadrant 1, find the following:
a. sin(A+B) I'm thinking it's something like 40/85 + 68/85 so it's sin(108/85) but then how do I get the exact answer, not some clumpy decinmal.
b. cos(A-B) same as above, or am I doing them wrong?
c. tan(2A)
d. sin(A/2)
I know that since A is in quad 3 then the cos is +, but that really doesn't help me all that much in solving it.


2) find the exact value of sin75 degrees.
Do I convert this one to radians and then do like I did in problem 3, or is there a different method for degrees?

3) find the exact value of tan pi/8. For this one I went through the identity going tan(pi/4)/2 which =(1-cos(pi/4))/(sin(pi/4)) but don't know where to go from there.


My teacher just doesn't explain things well(atleast not for me), and I really just don't know what I'm doing in this chapter. Can someone run through these step by step?

 

[Loren]

For 1, draw a sketch for angle A and a separate one for angle B. Use the Pythagorean Theorem to figure the measure of the third sides. Then use the identity sin(A+B)=sinA cosB + cosA sinB. Read off your sketches to determine the ratios of sinA, cosA, sinB and cosB, plug those into the right side of the identity and do the arithmetic.

For 2, the sin 75° = sin(150°/2). Draw a sketch of 150° and use the Pythagorean Theorem to determine that you are dealing with a 30-60 degree right triangle for which the ratios of the sides are easily determined. Use the identity \(\displaystyle \sin\frac{x}{2}=\pm\sqrt{\frac{1-\cos x}{2}}\) and do the plugging in and the arithmetic.

For 3, pi/8 is half of pi/4 and you know that pi/4 is a 45° angle for which the ratios are easily determined. Use techniques described in 1 and 2 above.